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The purpose of this paper is to present the investigation of the pressure-driven flow of aluminum oxide-water based nanofluid with the combined effect of entropy generation and radiative electro-magnetohydrodynamics filled with porous media inside a symmetric wavy channel.

The non-linear coupled differential equations are first converted into a number of ordinary differential equations with appropriate transformations and then analytical solutions are obtained by homotopic approach. Numerical simulation has been designed by the most efficient approach known homotopic-based Mathematica package BVPh 2.0 technique. The long wavelength approximation over the channel walls is taken into account. The obtained analytical results have been validated through graphs to infer the role of most involved pertinent parameters, whereas the characteristics of heat transfer and shear stress phenomena are presented and examined numerically.

It is found that the velocity profile decreases near to the channel. This is in accordance with the physical expectation because resistive force acts opposite the direction of fluid motion, which causes a decrease in velocity. It is seen that when the electromagnetic parameter increases then the velocity close to the central walls decreases whereas quite an opposite behavior is noted near to the walls. This happens because of the combined influence of electro-magnetohydrodynamics. It is perceived that by increasing the magnetic field parameter, Darcy number, radiation parameter, electromagnetic parameter and the temperature profile increases, and this is because of thermal buoyancy effect. For radiation and electromagnetic parameters, energy loss at the lower wall has substantial impact compared to the upper wall. Residual error minimizes at 20th order iterations.

The proposed prospective model is designed to explore the simultaneous effects of aluminum oxide-water base nanofluid, electro-magnetohydrodynamics and entropy generation through porous media. To the best of author’s knowledge, this model is reported for the first time.

Magnetohydrodynamic (MHD) nanoliquid are significant for thermal conductivity enhancement. The examination of heat transfer of crushing time-subordinate liquid flow past isometric surfaces has throughout the decades been a field of consideration for its wide scope of physical necessities: nourishment preparation, pressure, grease setup and hydrodynamic machines. Entropy generation in the squeezing flow of viscous nanomaterial is developed. MHD, Brownian motion and thermophoresis are considered. Porous space between the disks is taken. The analysis is carried out in the presence of radiation and viscous dissipation.

Nonlinear systems are reduced to an ordinary one through similarity variables. The convergent solution is developed by employing the homotopy analysis technique (HAM).

Convergent homotopic solutions are developed for the velocity, temperature and concentration. Entropy generation and Bejan number are explained. Skin friction and Nusselt number and Sherwood number are analyzed. For a higher approximation of porosity, parameter velocity is augmented. Temperature upsurges for larger thermophoresis and Brownian diffusion parameters. Concentration has an increasing effect on thermophoresis and Brownian diffusion parameters. For the rising value of the radiation parameter, both the Bejan number and entropy rate have increasing behaviors.

No such work is yet published in the literature.

The purpose of this paper is to review previous research studies on mathematical models for entropy generation in the magnetohydrodynamics (MHD) flow of nanofluids. In addition, the influence of various parameters on the velocity profiles, temperature profiles and entropy generation was studied. Furthermore, the numerical methods used to solve the model equations were summarized. The underlying purpose was to understand the research gap and develop a research agenda.

This paper reviews 141 journal articles published between 2010 and 2022 on topics related to mathematical models used to assess the impacts of various parameters on the entropy generation, heat transfer and velocity of the MHD flow of nanofluids.

This review clarifies the application of entropy generation mathematical models, identifies areas for future research and provides necessary information for future research in the development of efficient thermodynamic systems. It is hoped that this review paper can provide a basis for further research on the irreversibility of nanofluids flowing through different channels in the development of efficient thermodynamic systems.

Entropy generation analysis and minimization constitute effective approaches for improving the performance of thermodynamic systems. A comprehensive review of the effects of various parameters on entropy generation was performed in this study.

The purpose of this article is to analyze the heat and mass transfer with entropy generation during magnetohydrodynamics (MHD) flow of non-Newtonian Sisko nanofluid over a linearly stretching cylinder under the influence of velocity slip, chemical reaction and thermal radiation. The Brownian motion, thermophoresis and activation energy are assimilated in this nanofluid model. Convective boundary conditions on heat and mass transfer are considered. The physical model may have diverse applications in several areas of technology underlying thermohydrodynamics including supercritical fluid extraction, refrigeration, ink-jet printing and so on.

The dimensional governing equations are nondimensionalized by using appropriate similarity variables. The resulting boundary value problem is converted into initial value problem using the method of superposition and numerically computed by employing well-known fourth-order Runge–Kutta–Fehlberg approach along with shooting technique (RKF4SM). The quantitative impacts of emerging physical parameters on the velocity, temperature, concentration, skin friction coefficient, Nusselt number, Sherwood number, entropy generation rate and Bejan number are presented graphically and in tabular form, and the salient features are comprehensively discussed.

From graphical outcomes, it is concluded that the slip parameters greatly influence the flow characteristics. Fluid temperature is elevated with rising radiation parameter and thermal Biot number. Nanoparticle concentration is reported in decreasing form with activation energy parameter. Entropy is found to be an increasing function of magnetic field, Brownian motion and material parameters. The entropy is less generated for shear-thinning fluid compared to shear-thickening as well as Newtonian fluids in the system.

Till now no study has been documented to explore the impact of binary chemical reaction with Arrhenius activation energy on entropy generation in an MHD boundary layer flow of non-Newtonian Sisko nanofluid over a linear stretching cylinder with velocity slip and convective boundary conditions.

The study aims to investigate magnetohydrodynamics thermal convection energy transference and entropy production in an open chamber saturated with ferrofluid having an isothermal solid block.

Analysis of thermal convection phenomenon was performed for an open chamber saturated with a nanofluid having an isothermal solid unit placed inside the cavity with various aspect ratios. The left border temperature is kept at T_c. An external cooled nanofluid of fixed temperature T_c penetrates into the domain from the right open border. The nanofluid circulation is Newtonian, incompressible, and laminar. The uniform magnetic field of strength B at the tilted angle of γ is applied. The finite volume technique is used to work out the non-linear equations of liquid motion and energy transport. For Rayleigh number (Ra=1e+7), numerical simulations were executed for varying the solid volume fractions of the nanofluid (ϕ = 0.01–0.04), the aspect ratios of a solid body (A_s = 0.25–4), the Hartmann number (Ha = 0–100), the magnetic influence inclination angle (γ = 0–π/2) and the non-dimensional temperature drop (Ω = 0.001–0.1) on the liquid motion, heat transference and entropy production.

Numerical outcomes are demonstrated by using isolines of temperature and stream function, profiles of mean Nusselt number and entropy generations. The results indicate that the entropy generation rate and mean Nu can be decreased with an increase in Ha. The inner solid block of A_s = 0.25 reflects the maximum heat transfer rate in comparison with other considered blocks. The addition of nano-sized particles results in a growth of energy transport and mean entropy generations.

An efficient computational technique has been developed to solve natural convection problem for an open chamber. The originality of this research is to scrutinize the convective transport and entropy production in an open domain with inner body. The outcomes would benefit scientists and engineers to become familiar with the investigation of convective energy transference and entropy generation in open chambers with inner bodies, and the way to predict the energy transference strength in the advanced engineering systems.

Nonlinear mixed-convective entropy optimized the flow of hyperbolic-tangent nanofluid (HTN) with magnetohydrodynamics (MHD) process is considered over a vertical slendering surface. The impression of activation energy is incorporated in the modeling with the significance of nonlinear radiation, dissipative-function, heat generation/consumption connection and Joule heating. Research in this area has practical applications in the design of efficient heat exchangers, thermal management systems or nanomaterial-based devices.

Suitable set of variables is introduced to transform the PDEs (Partial differential equations) system into required ODEs (Ordinary differential equations) system. The transformed ODEs system is then solved numerically via finite difference method. Graphical artworks are made to predict the control of applicable transport parameters on surface entropy, Bejan number, Sherwood number, skin-friction, Nusselt number, temperature, velocity and concentration fields.

It is noticed from present numerical examination that Bejan number aggravates for improved estimations of concentration-difference parameter a_2, Eckert number E_c, thermal ratio parameter ?_w and radiation parameter R_d, whereas surface entropy condenses for flow performance index n, temperature-difference parameter a_1, thermodiffusion parameter N_t and mixed convection parameter ?. Sherwood number is enriched with the amplification of pedesis-motion parameter N_b, while opposite development is perceived for thermodiffusion parameter. Lastly, outcomes are matched with formerly published data to authenticate the present numerical investigation.

To the best of the authors' knowledge, no investigation has been reported yet that explains the entropic behavior with activation energy in the flowing of hyperbolic-tangent mixed-convective nanomaterial due to a vertical slendering surface.

The purpose of this study is to analyze the entropy generation in magnetohydrodynamics stagnation point mixed convection flow of Carreau nanofluid through porous medium.

The system is solved using the homotopy scheme.

Minimizing radiation, magnetic, permeability and temperature difference parameters responds to minimizing entropy production.

To the best of the authors’ knowledge, no such analysis has yet been reported.

This study aims to investigate the influence of wall curvature in a semicircular thermal annular system on magneto-nanofluidic flow, heat transfer and entropy generation. The analysis is conducted under constant cooling surface and fluid volume constraints.

The mathematical equations describing the thermo-fluid flow in the semicircular system are solved using the finite element technique. Four different heating wall configurations are considered, varying the undulation numbers of the heated wall. Parametric variations of bottom wall undulation (f), buoyancy force characterized by the Rayleigh number (Ra), magnetic field strength represented by the Hartmann number (Ha) and inclination of the magnetic field (γ) on the overall thermal performance are studied extensively.

This study reveals that the fluid circulation strength is maximum in the case of a flat bottom wall. The analysis shows that the bottom wall contour and other control parameters significantly influence fluid flow, entropy production and heat transfer. The modified heated wall with a single undulation exhibits the highest entropy production and thermal convection, leading to a heat transfer enhancement of up to 21.85% compared to a flat bottom. The magnetic field intensity and orientation have a significant effect on heat transfer and irreversibility production.

Further research can explore a wider range of parameter values, alternative heating wall profiles and boundary conditions to expand the understanding of magneto-nanofluidic flow in semicircular thermal systems.

This study introduces a constraint-based analysis of magneto-nanofluidic thermal behavior in a complex semicircular thermal system, providing insights into the impact of wall curvature on heat transfer performance. The findings contribute to the design and optimization of thermal systems in various applications.

The purpose of this paper is to evaluate the temperature, the Dirichlet conditions have been considered to the parallel horizontal plates. The model of generalized Brinkman-extended Darcy with the Boussinesq approximation is considered and the governing equations are computed by COMSOL multiphysics.

In the current study, the thermodynamic irreversible principle is applied to study the unsteady Poiseuille–Rayleigh–Bénard (PRB) mixed convection in a channel (aspect ratio A = 5), with the effect of a uniform transverse magnetic field.

The effects of various flow parameters on the fluid flow, Hartmann number (Ha), Darcy number (Da), Brinkman number (Br) and porosity (ε), are presented graphically and discussed. Numerical results for temperature and velocity profiles, entropy generation variations and contour maps of streamlines, are presented as functions of the governing parameter mentioned above. Basing on the generalized Brinkman-extended Darcy formulation, which allows the satisfaction of the no-slip boundary condition on a solid wall, it is found that the flow field and then entropy generation is notably influenced by the considering control parameters. The results demonstrate that the flow tends toward the steady-state with four various regimes, which strongly depends on the Hartman and Darcy numbers variations. Local thermodynamic irreversibilities are more confined near the active top and bottom horizontal walls of the channel when increasing the Da and decreasing the Hartmann number. Entropy generation is also found to be considerably affected by Brinkman number variation.

In the present work, we are presenting our investigations on the influence of a transverse applied external magnetohydrodynamic on entropy generation at the unsteady laminar PRB flow of an incompressible, Newtonian, viscous electrically conducting binary gas mixture fluid in porous channel of two horizontal heated plates. The numerical solutions for the liquid velocity, the temperature distribution and the rates of heat transport and entropy generation are obtained and are plotted graphically.

A parabolic trough solar collector is an advanced concentrated solar power technology that significantly captures radiant energy. Solar power will help different sectors reach their energy needs in areas where traditional fuels are in use. This study aims to examine the sensitivity analysis for optimizing the heat transfer and entropy generation in the Jeffrey magnetohydrodynamic hybrid nanofluid flow under the influence of motile gyrotactic microorganisms with solar radiation in the parabolic trough solar collectors. The influences of viscous dissipation and Ohmic heating are also considered in this investigation.

Governing partial differential equations are derived via boundary layer assumptions and nondimensionalized with the help of suitable similarity transformations. The resulting higher-order coupled ordinary differential equations are numerically investigated using the Runga-Kutta fourth-order numerical approach with the shooting technique in the computational MATLAB tool.

The numerical outcomes of influential parameters are presented graphically for velocity, temperature, entropy generation, Bejan number, drag coefficient and Nusselt number. It is observed that escalating the values of melting heat parameter and the Prandl number enhances the Nusselt number, while reverse effect is observed with an enhancement in the magnetic field parameter and bioconvection Lewis number. Increasing the magnetic field and bioconvection diffusion parameter improves the entropy and Bejan number.

Nanotechnology has captured the interest of researchers due to its engrossing performance and wide range of applications in heat transfer and solar energy storage. There are numerous advantages of hybrid nanofluids over traditional heat transfer fluids. In addition, the upswing suspension of the motile gyrotactic microorganisms improves the hybrid nanofluid stability, enhancing the performance of the solar collector. The use of solar energy reduces the industry’s dependency on fossil fuels.